Spectrum of the effective SU(3) Hamiltonian in a small volume computed by path-integral Monte Carlo integration

Using a simple Monte Carlo integration method for quantum-mechanical problems on a ''time lattice'' the mass gaps of the low-lying states of Luescher's effective Hamiltonian with and without massless fermions for a small volume are computed. While there is good agreement between this method and previous Rayleigh-Ritz-type calculations in the case of SU(2), notable differences are found in the case of SU(3) for most states. The statistical and systematic errors are competitive with those of the variational method. Having no dependence on basis set size, the Monte Carlo method is a good alternative to the Rayleigh-Ritz calculations also for SU(3). An extension of the method to intermediate volumes including fermions is definitely possible